Harmonic surfaces in the Cayley plane

Abstract

We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane OP2=F4/Spinfalse(9false). By exhibiting this symmetric space as a submanifold of the Grassmannian of 10‐dimensional subspaces of the fundamental representation of F4, techniques and constructions similar to those used in earlier works on twistor constructions of nilconformal harmonic maps into classical Grassmannians can also be applied in this case. The originality of our approach lies on the use of the classification of nilpotent orbits in Lie algebras as described by Djoković.